The following is an action performable by a Stone Golem.
"Slow (Recharge 5-6): The golem Targets one or more creatures it can see within 10 ft. of it. Each target must make a DC 17 Wisdom saving throw against this magic. On a failed save, a target can't use Reactions, its speed is halved, and it can't make more than one Attack on its turn. In addition, the target can take either an action or a Bonus Action on its turn, not both. These Effects last for 1 minute. A target can repeat the saving throw at the end of each of its turns, Ending the Effect on itself on a success."
How does a player remove this effect outside of passing the saving throw?
The following ability belongs to the Vargouille:
"Kiss. The vargouille kisses one incapacitated humanoid within 5 feet of it. The target must succeed on a DC 12 Charisma saving throw or become cursed. The cursed target loses l point of Charisma after each hour, as its head takes on fiendish aspects. The curse doesn't advance while the target is in sunlight or the area of a daylight spell; don't count that time. When the cursed target's Charisma becomes 2, it dies, and its head tears from its body and becomes a new vargouille. Casting remove curse, greater restoration, or a similar spell on the target before the transformation is complete can end the curse. Doing so undoes the changes made to the target by the curse."
The fluff of the vargouille states the following:
"Each vargouille carries a disease that creates more of its kind;"
How does a Paladin's Divine Health and Lay of Hands abilities interact with the Vargouille's kiss?
The Slow effect from the Stone Golem says exactly how it can be removed: wait 1 minute or make a successful saving throw before then. The speed impairment (but not the remainder of the effect) can be negated by Freedom of Movement.
With regard to the Vargouille's Kiss, a DM could rule otherwise, but the effect itself refers to the Kiss being a curse, not a disease. The wording of the flavour text is unfortunate, but otherwise the effect seems designed to subvert immunity to disease and/or the broad availability of disease-curing effects.
For the golem, I think making the save is the only way. The golem doesn't actually cast the Slow spell, they just create the same effect. So Dispel Magic won't work. I'm certain a Wish spell could end the effect, though that's fairly excessive. Casting the Resistance cantrip on the slowed party member would give them a boost to their next save, which could help them break it.
For the Paladin, Divine Health and Lay On Hands have no effect on curses. The fluff text is just that, when it comes to the mechanics you go with what's in the stat block. So mechanically, the effect is a curse not a disease.
Edit: to be clear, there is no "Diseased condition" in the sense of PHB Appendix A (like Poisoned or Paralyzed). But the above link includes monsters like Slaads that induce disease that can be cured as diseases. (It also includes monsters with disease referenced elsewhere in their statbox, but that's easy to see.)
The following is an action performable by a Stone Golem.
"Slow (Recharge 5-6): The golem Targets one or more creatures it can see within 10 ft. of it. Each target must make a DC 17 Wisdom saving throw against this magic. On a failed save, a target can't use Reactions, its speed is halved, and it can't make more than one Attack on its turn. In addition, the target can take either an action or a Bonus Action on its turn, not both. These Effects last for 1 minute. A target can repeat the saving throw at the end of each of its turns, Ending the Effect on itself on a success."
How does a player remove this effect outside of passing the saving throw?
The following ability belongs to the Vargouille:
"Kiss. The vargouille kisses one incapacitated humanoid within 5 feet of it. The target must succeed on a DC 12 Charisma saving throw or become cursed. The cursed target loses l point of Charisma after each hour, as its head takes on fiendish aspects. The curse doesn't advance while the target is in sunlight or the area of a daylight spell; don't count that time. When the cursed target's Charisma becomes 2, it dies, and its head tears from its body and becomes a new vargouille. Casting remove curse, greater restoration, or a similar spell on the target before the transformation is complete can end the curse. Doing so undoes the changes made to the target by the curse."
The fluff of the vargouille states the following:
"Each vargouille carries a disease that creates more of its kind;"
How does a Paladin's Divine Health and Lay of Hands abilities interact with the Vargouille's kiss?
The Slow effect from the Stone Golem says exactly how it can be removed: wait 1 minute or make a successful saving throw before then. The speed impairment (but not the remainder of the effect) can be negated by Freedom of Movement.
With regard to the Vargouille's Kiss, a DM could rule otherwise, but the effect itself refers to the Kiss being a curse, not a disease. The wording of the flavour text is unfortunate, but otherwise the effect seems designed to subvert immunity to disease and/or the broad availability of disease-curing effects.
Even a blind squirrel finds a nut once in awhile.
For the golem, I think making the save is the only way. The golem doesn't actually cast the Slow spell, they just create the same effect. So Dispel Magic won't work. I'm certain a Wish spell could end the effect, though that's fairly excessive. Casting the Resistance cantrip on the slowed party member would give them a boost to their next save, which could help them break it.
For the Paladin, Divine Health and Lay On Hands have no effect on curses. The fluff text is just that, when it comes to the mechanics you go with what's in the stat block. So mechanically, the effect is a curse not a disease.
Thank you. I would like to inquire further regarding disease. Do you know of a monster that does inflict a disease condition?
start here: https://www.dndbeyond.com/search?q=disease&f=monsters&c=monsters
Edit: to be clear, there is no "Diseased condition" in the sense of PHB Appendix A (like Poisoned or Paralyzed). But the above link includes monsters like Slaads that induce disease that can be cured as diseases. (It also includes monsters with disease referenced elsewhere in their statbox, but that's easy to see.)
Even a blind squirrel finds a nut once in awhile.